Finite Group Databasebeta

← C2×#21457387 #30555056

Subgroups — C2×#21457387 #30555056

Order 15616.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519807C211yesmaximal, characteristic, complemented
2C22×Q16×D61C211yesmaximal, characteristic, complemented
3C2×#16840425C211yesmaximal, characteristic, complemented
4C2×#16840419C211yesmaximal, characteristic
5#21457387C2116yesmaximal, direct product factor
6C2×#16840153C211yesmaximal, characteristic, complemented
7C2×#16840018C211yesmaximal, characteristic, complemented
8C2×#16839990C211yesmaximal, characteristic, complemented
9C2×#16839983C211yesmaximal, characteristic, complemented
10C2×#16839970C211yesmaximal, characteristic, complemented
11C2×#16839920C211yesmaximal, characteristic, complemented
12C2×#16839919C211yesmaximal, characteristic, complemented
13C2×#16839899C211yesmaximal, characteristic, complemented
14C2×#16839866C211yesmaximal, characteristic, complemented
15C2×#16839836C211yesmaximal, characteristic, complemented
16C2×C61×#452C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×Q8×D61C2211yescharacteristic
20C2×#14519807—28no—
21C2×#14519807C2218yescomplemented
22C22×Dic244C2211yescharacteristic
23C22×Dic244C2211yescharacteristic
24C22×#11758202C2211yescharacteristic
25C22×#11758202C2211yescharacteristic
26C22×#11758202C2211yescharacteristic
27C2×Q16×D61—28no—
28C2×Q16×D61C2218yescomplemented
29C22×#11758200C2211yescharacteristic
30C22×#11758200C2211yescharacteristic
31C22×#11758194C2211yescharacteristic
32C22×C8×D61C2211yescharacteristic
33#16840425—24no—
34#16840425C2218yescomplemented
35#16840419—24no—
36#16840419C2218yes—
37C2×#14519776—21no—
38C2×#14519775C2211yescharacteristic
39C2×#14519764—21no—
40C2×#14519764C2211yescharacteristic
41C2×#14519757C2211yescharacteristic
42C2×#14519756—21no—
43C2×#14519756C2211yescharacteristic
44C2×#14519755—21no—
45C2×#14519754—21no—
46C2×#14519748—21no—
47C2×#14519748C2211yescharacteristic
48C2×Q8×Dic61C2211yescharacteristic
49C2×#14519742C2211yescharacteristic
50C2×C4×C22⋊D61—21no—
51C2×C4×C22⋊D61C2211yescharacteristic
52C2×#14519737—21no—
53#16840153C2218yescomplemented
54#16840018C2218yescomplemented
55#16839990C2218yescomplemented
56#16839983C2218yescomplemented
57#16839970C2218yescomplemented
58#16839920C2218yescomplemented
59#16839919C2218yescomplemented
60#16839899C2218yescomplemented
61#16839866C2218yescomplemented
62#16839836C2218yescomplemented
63C2×#14519708C2211yescharacteristic
64C2×#14519706C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519702C2211yescharacteristic
67C2×#14519701C2211yescharacteristic
68C2×#14519700C2211yescharacteristic
69C2×#14519689C2211yescharacteristic
70C2×#14519687C2211yescharacteristic
71C22×#41×C61C2211yescharacteristic
72C22×Q16×C61C2211yescharacteristic
73C22×SD16×C61C2211yescharacteristic
74C2×C22⋊Q8×C61C2211yescharacteristic
75C61×#452C2218yescomplemented
76C2×#103×C61C2211yescharacteristic
77C2×#102×C61C2211yescharacteristic
78C2×C22⋊C8×C61C2211yescharacteristic
79C22×Dic122—24no—
80C22×Dic122—21no—
81C22×Dic122—22no—
82C22×Dic122—21no—
83C22×Dic122—21no—
84C22×Dic122—42no—
85C22×Dic122C2311yescharacteristic
86C22×Dic122C2311yescharacteristic
87C22×Dic122C2314yes—
88C22×Dic122C2311yescharacteristic
89C2×Q8×D61—22no—
90C2×Q8×D61—22no—
91C2×Q8×D61—24no—
92C2×Q8×D61—24no—
93C2×Q8×D61—42no—
94C2×Q8×D61—42no—
95C2×Q8×D61C2314yes—
96C2×Q8×D61C2314yes—
97C22×C22⋊D61—21no—
98C22×C22⋊D61D411yescharacteristic
99C23×Dic61—21no—
100C22×C4×D61—21no—
101C22×C4×D61—21no—
102C22×C4×D61C2311yescharacteristic
103#14519807—232no—
104C2×Dic244—24no—
105C2×Dic244—42no—
106C2×Dic244C2314yes—
107C2×Dic244C2314yes—
108C2×#11758202—24no—
109C2×#11758202—24no—
110C2×#11758202D418yescomplemented
111C2×#11758202C2314yes—
112C2×#11758202C2314yes—
113C2×#11758202C2314yes—
114Q16×D61—232no—
115C2×#11758200—24no—
116C2×#11758200—24no—
117C2×#11758200C2314yes—
118C2×#11758200C2314yes—
119C2×#11758194—24no—
120C2×#11758194C2314yes—
121C22×#92418C2311yescharacteristic
122C22×#92418C2311yescharacteristic
123C2×C8×D61—24no—
124C2×C8×D61C2314yes—
125#14519776—28no—
126#14519775—22no—
127#14519775C2314yes—
128#14519764—28no—
129#14519764—22no—
130#14519764C2314yes—
131#14519757—22no—
132#14519757C2314yes—
133#14519756—22no—
134#14519756—28no—
135#14519756C2314yes—
136#14519755—28no—
137#14519754—28no—
138#14519748—28no—
139#14519748—22no—
140#14519748C2314yes—
141Q8×Dic61—22no—
142Q8×Dic61C2314yes—
143#14519742—22no—
144#14519742C2314yes—
145C4×C22⋊D61—28no—
146C4×C22⋊D61D414yes—
147C4×C22⋊D61C2314yes—
148#14519737—28no—
149C2×C4⋊Dic61—21no—
150C2×C4⋊Dic61—21no—
151C2×C4⋊Dic61C2311yescharacteristic
152C2×#11758196—21no—
153C2×#11758196—21no—
154C2×#11758196—21no—
155C2×#11758196—21no—
156C2×#11758196D411yescharacteristic
157C2×C22⋊Dic61—21no—
158C2×C22⋊Dic61—21no—
159C2×C22⋊Dic61—21no—
160C2×C22⋊Dic61—21no—
161C2×C22⋊Dic61D411yescharacteristic
162C2×#11758198—21no—
163C2×#11758198D411yescharacteristic
164C2×C4×Dic61—21no—
165C2×C4×Dic61—21no—
166C2×C4×Dic61C2311yescharacteristic
167#14519708C2314yes—
168#14519706C2314yes—
169#14519702C2314yes—
170#14519702C2314yes—
171#14519701C2314yes—
172#14519700C2314yes—
173#14519689C2314yes—
174#14519687C2314yes—
175C2×#41×C61—22no—
176C2×#41×C61—24no—
177C2×#41×C61—42no—
178C2×#41×C61C2314yes—
179C22×Q8×C61C2311yescharacteristic
180C22×Q8×C61C2311yescharacteristic
181C22×D4×C61—21no—
182C22×D4×C61C2311yescharacteristic
183C23×C4×C61—21no—
184C23×C4×C61C2311yescharacteristic
185C2×Q16×C61—24no—
186C2×Q16×C61C2314yes—
187C2×SD16×C61—42no—
188C2×SD16×C61C2314yes—
189C22×C8×C61C2311yescharacteristic
190C22×C8×C61C2311yescharacteristic
191C22⋊Q8×C61—22no—
192C22⋊Q8×C61C2314yes—
193C2×C4⋊C4×C61—21no—
194C2×C4⋊C4×C61C2311yescharacteristic
195C2×C22⋊C4×C61—21no—
196#103×C61C2314yes—
197#102×C61C2314yes—
198C22⋊C8×C61C2314yes—
199C24×C61—21no—
200C24×C61C2×D411yescharacteristic
201C23×D61C2×D411yescharacteristic
202#41×C61—28no—
203#41×C61—44no—
204#41×C61—48no—
205C2×Q8×C61—21no—
206C2×Q8×C61—21no—
207C2×Q8×C61—22no—
208C2×Q8×C61—22no—
209C2×Q8×C61—22no—
210C2×Q8×C61C2×D414yes—
211C2×Q8×C61C2412yes—
212C2×Q8×C61C2412yes—
213C2×D4×C61—24no—
214C2×D4×C61—22no—
215C2×D4×C61—21no—
216C2×D4×C61—22no—
217C2×D4×C61—44no—
218C2×D4×C61C2412yes—
219C22×C4×C61—21no—
220C22×C4×C61—22no—
221C22×C4×C61—22no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—24no—
225C22×C4×C61—44no—
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2412yes—
229C22×C4×C61C2411yescharacteristic
230C2×C22⋊D61—24no—
231C2×C22⋊D61—24no—
232C2×C22⋊D61—44no—
233C2×C22⋊D61C2×D414yes—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—24no—
238C22×Dic61—21no—
239C22×Dic61—44no—
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243Q8×D61—28no—
244Q8×D61—28no—
245Q8×D61—44no—
246Q8×D61—44no—
247Q8×D61—48no—
248Q8×D61—48no—
249C2×C4×D61—22no—
250C2×C4×D61—22no—
251C2×C4×D61—24no—
252C2×C4×D61—24no—
253C2×C4×D61—44no—
254C2×C4×D61—44no—
255C2×C4×D61C2×D412yes—
256C2×C4×D61C2412yes—
257C2×Dic122—21no—
258C2×Dic122—22no—
259C2×Dic122—22no—
260C2×Dic122—22no—
261C2×Dic122—22no—
262C2×Dic122—22no—
263C2×Dic122—28no—
264C2×Dic122—21no—
265C2×Dic122—24no—
266C2×Dic122—21no—
267C2×Dic122—24no—
268C2×Dic122—24no—
269C2×Dic122—44no—
270C2×Dic122—48no—
271C2×Dic122—44no—
272C2×Dic122—44no—
273C2×Dic122—44no—
274C2×Dic122C2×D414yes—
275C2×Dic122C2412yes—
276C2×Dic122C2412yes—
277C2×Dic122C2412yes—
278Q16×C61—28no—
279SD16×C61—44no—
280C2×C8×C61—22no—
281C2×C8×C61—22no—
282C2×C8×C61C2412yes—
283C2×C8×C61C2412yes—
284C4⋊C4×C61—24no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61C2412yes—
287C22⋊C4×C61—24no—
288C22⋊Dic61—24no—
289C22⋊Dic61—24no—
290C22⋊Dic61—24no—
291C22⋊Dic61—24no—
292C22⋊Dic61C2×D414yes—
293#11758202—28no—
294#11758202—28no—
295#11758202C2×D4116yescomplemented
296#11758200—28no—
297#11758200—28no—
298#11758198—24no—
299#11758198C2×D414yes—
300C4⋊Dic61—21no—
301C4⋊Dic61—24no—
302C4⋊Dic61—24no—
303C4⋊Dic61C2412yes—
304#11758196—24no—
305#11758196—24no—
306#11758196—24no—
307#11758196—24no—
308#11758196C2×D414yes—
309C4×Dic61—24no—
310C4×Dic61—24no—
311C4×Dic61C2×D412yes—
312C4×Dic61C2412yes—
313#11758194—28no—
314C2×#92418—22no—
315C2×#92418C2×D414yes—
316C2×#92418C2412yes—
317C2×#92418C2412yes—
318Dic244—28no—
319Dic244—44no—
320C8×D61—28no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—42no—
326C23×C61—42no—
327C23×C61—42no—
328C23×C61C22×D412yes—
329C23×C61C22×D411yescharacteristic
330C22×D61—22no—
331C22×D61—22no—
332C22×D61#13714yescomplemented
333C22×D61C22×D412yes—
334Q8×C61—24no—
335Q8×C61—22no—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—42no—
339Q8×C61C22×D414yes—
340D4×C61—22no—
341D4×C61—22no—
342D4×C61—48no—
343D4×C61—42no—
344C2×C4×C61—22no—
345C2×C4×C61—24no—
346C2×C4×C61—22no—
347C2×C4×C61—24no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—48no—
353C2×C4×C61—42no—
354C2×C4×C61—42no—
355C2×C4×C61C22×D412yes—
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D412yes—
358C2×C4×C61H(5,𝔽2)12yes—
359C2×C4×C61C2511yescharacteristic
360C22⋊D61—28no—
361C22⋊D61—48no—
362C2×Dic61—24no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—48no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61C22×D412yes—
375C2×Dic61C22×D412yes—
376C2×Dic61C22×D412yes—
377C4×D61—24no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—48no—
381C4×D61—48no—
382Dic122—24no—
383Dic122—22no—
384Dic122—22no—
385Dic122—22no—
386Dic122—22no—
387Dic122—22no—
388Dic122—48no—
389Dic122—48no—
390Dic122—48no—
391Dic122—42no—
392Dic122—42no—
393Dic122C22×D414yes—
394C8×C61—22no—
395C8×C61—22no—
396#92418—22no—
397#92418C22×D414yes—
398C2×#3270—611nomaximal, Sylow
399C22×C61—22no—
400C22×C61—22no—
401C22×C61—22no—
402C22×C61—44no—
403C22×C61—42no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—84no—
407C22×C61D4212yes—
408C22×C61C2×#13712yes—
409C22×C61#57812yes—
410C22×C61C23×D411yescharacteristic
411C2×D61—22no—
412C2×D61—28no—
413C2×D61—22no—
414C2×D61C2×#13714yescomplemented
415C4×C61—22no—
416C4×C61—24no—
417C4×C61—42no—
418C4×C61—42no—
419C4×C61D4212yes—
420C4×C61C23×D411yescharacteristic
421C4×C61C2×H(5,𝔽2)11yescharacteristic
422Dic61—24no—
423Dic61—22no—
424Dic61—22no—
425Dic61—22no—
426Dic61—42no—
427Dic61—42no—
428Dic61—42no—
429C22×#137—611no—
430C23×Q16—611no—
431C2×D4×Q8—611no—
432C2×#548—611no—
433#3270—6116no—
434C2×#497—611no—
435C2×#470—611no—
436C2×#465—611no—
437C2×#464—611no—
438C2×#462—611no—
439C2×#452D6111yescharacteristic, complemented
440C2×#451—611no—
441C2×#451—611no—
442C2×#448—611no—
443C2×#441—611no—
444C2×#435—611no—
445C2×C61—42no—
446C2×C61—82no—
447C2×C61#327014yescomplemented
448C2×C61C2×D4211yescharacteristic
449C2×C61C22×#13711yescharacteristic
450C2×C61C2×#57811yescharacteristic
451D61—24no—
452C22×#41C2×D6111yescharacteristic
453C23×Q8—611no—
454C23×Q8—611no—
455C23×Q8—611no—
456C2×#137—618no—
457C2×#137—1228no—
458C22×Q16—611no—
459C22×Q16—611no—
460C22×Q16—611no—
461C22×Q16—618no—
462C22×Q16—611no—
463C22×Q16—611no—
464C22×Q16—1228no—
465C22×Q16C2×D6111yescharacteristic
466C22×SD16—611no—
467C22×SD16—611no—
468C22×SD16C2×D6111yescharacteristic
469C22×M16—611no—
470C23×C8—611no—
471D4×Q8—618no—
472D4×Q8—1224no—
473#548—618no—
474#548—1224no—
475C2×C4⋊Q8—611no—
476C2×C4⋊Q8—1221no—
477C2×#124—611no—
478C2×#124—1221no—
479C2×C22⋊Q8—611no—
480C2×C22⋊Q8—611no—
481C2×C22⋊Q8—1221no—
482C2×C22⋊Q8—1221no—
483C2×C22⋊Q8—1221no—
484C2×C22⋊Q8C2×D6111yescharacteristic
485C2×#121—611no—
486C2×#121—1221no—
487C2×C4×Q8—611no—
488C2×C4×Q8—611no—
489C2×C4×D4—611no—
490C2×C4×D4—1221no—
491C2×C4×D4—1221no—
492#497—618no—
493#470—618no—
494#465—618no—
495#464—618no—
496#462—618no—
497#452C2×D6118yescomplemented
498#451—618no—
499#451—618no—
500#448—618no—
501#441—618no—
502#435—618no—
503C2×#106—611no—
504C2×C4⋊C8—611no—
505C2×#103—611no—
506C2×#103—611no—
507C2×#103—611no—
508C2×#103—611no—
509C2×#103C2×D6111yescharacteristic
510C2×#102C2×D6111yescharacteristic
511C2×C22⋊C8—611no—
512C2×C22⋊C8C2×D6111yescharacteristic
513C2×#97—611no—
514C61C2×#327011yescharacteristic, complemented, Sylow
515C2×#41—22no—
516C2×#41—24no—
517C2×#41—42no—
518C2×#41C22×D6114yes—
519C22×Q8—614no—
520C22×Q8—614no—
521C22×Q8—611no—
522C22×Q8—611no—
523C22×Q8—611no—
524C22×Q8—614no—
525C22×Q8—1221no—
526C22×Q8—1221no—
527C22×Q8—1224no—
528C22×Q8—1222no—
529C22×Q8—1222no—
530C22×Q8—1221no—
531C22×Q8—1222no—
532C22×Q8—1224no—
533C22×Q8—1224no—
534C22×Q8—2442no—
535C22×Q8—2442no—
536C22×Q8—2442no—
537C22×Q8C22×D6111yescharacteristic
538C22×Q8C22×D6111yescharacteristic
539C22×D4—21no—
540C22×D4—611no—
541C22×D4—1221no—
542C22×D4C22×D6111yescharacteristic
543C23×C4—21no—
544C23×C4—611no—
545C23×C4—1221no—
546C23×C4—1221no—
547C23×C4—1221no—
548C23×C4C22×D6111yescharacteristic
549#137—12232no—
550C2×Q16—24no—
551C2×Q16—618no—
552C2×Q16—614no—
553C2×Q16—614no—
554C2×Q16—614no—
555C2×Q16—614no—
556C2×Q16—614no—
557C2×Q16—1224no—
558C2×Q16—1224no—
559C2×Q16—12232no—
560C2×Q16—1224no—
561C2×Q16—2442no—
562C2×Q16C22×D6114yes—
563C2×SD16—42no—
564C2×SD16—614no—
565C2×SD16—614no—
566C2×SD16—1224no—
567C2×SD16—1224no—
568C2×SD16C22×D6114yes—
569C2×M16—614no—
570C2×M16—1224no—
571C22×C8—611no—
572C22×C8—611no—
573C22×C8—614no—
574C22×C8—1224no—
575C22×C8C22×D6111yescharacteristic
576C22×C8C22×D6111yescharacteristic
577C4⋊Q8—614no—
578C4⋊Q8—1222no—
579C4⋊Q8—1228no—
580#124—614no—
581#124—1222no—
582#124—1228no—
583C22⋊Q8—22no—
584C22⋊Q8—614no—
585C22⋊Q8—614no—
586C22⋊Q8—1228no—
587C22⋊Q8—1228no—
588C22⋊Q8—1222no—
589C22⋊Q8—1228no—
590C22⋊Q8—1222no—
591C22⋊Q8C22×D6114yes—
592#121—614no—
593#121—1222no—
594#121—1228no—
595C4×Q8—614no—
596C4×Q8—614no—
597C4×Q8—1222no—
598C4×Q8—1222no—
599C4×D4—614no—
600C4×D4—614no—
601C4×D4—1228no—
602C4×D4—1228no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—1221no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4—1221no—
610C2×C4⋊C4—1221no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4C22×D6111yescharacteristic
613C2×C22⋊C4—21no—
614C2×C22⋊C4—611no—
615C2×C22⋊C4—611no—
616C2×C22⋊C4—1221no—
617C2×C22⋊C4—1221no—
618C2×C22⋊C4—1221no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C42—611no—
622C2×C42—1221no—
623C2×C42—1221no—
624#106—614no—
625C4⋊C8—614no—
626#103—614no—
627#103—614no—
628#103—614no—
629#103—614no—
630#103C22×D6114yes—
631#102C22×D6114yes—
632C22⋊C8—614no—
633C22⋊C8C22×D6114yes—
634#97—614no—
635C24—21no—
636C24—611no—
637C24D4×D6111yescharacteristic
638#41—28no—
639#41—44no—
640#41—48no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—22no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—614no—
647C2×Q8—612no—
648C2×Q8—612no—
649C2×Q8—612no—
650C2×Q8—1224no—
651C2×Q8—1224no—
652C2×Q8—1228no—
653C2×Q8—1221no—
654C2×Q8—1221no—
655C2×Q8—1224no—
656C2×Q8—1221no—
657C2×Q8—1222no—
658C2×Q8—1228no—
659C2×Q8—1228no—
660C2×Q8—1222no—
661C2×Q8—1222no—
662C2×Q8—1222no—
663C2×Q8—1222no—
664C2×Q8—2444no—
665C2×Q8—2444no—
666C2×Q8—2444no—
667C2×Q8—2448no—
668C2×Q8—2444no—
669C2×Q8—2444no—
670C2×Q8—2444no—
671C2×Q8—2448no—
672C2×Q8—2448no—
673C2×Q8D4×D6114yes—
674C2×Q8C23×D6112yes—
675C2×Q8C23×D6112yes—
676C2×D4—24no—
677C2×D4—22no—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—44no—
681C2×D4—614no—
682C2×D4—1224no—
683C2×D4—1224no—
684C2×D4—2444no—
685C2×D4C23×D6112yes—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—24no—
692C22×C4—44no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—612no—
697C22×C4—612no—
698C22×C4—1224no—
699C22×C4—1224no—
700C22×C4—1221no—
701C22×C4—1222no—
702C22×C4—1222no—
703C22×C4—1224no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—2444no—
708C22×C4—2444no—
709C22×C4—2444no—
710C22×C4D4×D6112yes—
711C22×C4D4×D6111yescharacteristic
712C22×C4C23×D6112yes—
713C22×C4C23×D6111yescharacteristic
714Q16—28no—
715Q16—6116no—
716Q16—1228no—
717Q16—1228no—
718Q16—1228no—
719Q16—2444no—
720SD16—44no—
721SD16—1228no—
722SD16—1228no—
723M16—1228no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—614no—
727C2×C8—612no—
728C2×C8—612no—
729C2×C8—1228no—
730C2×C8—1222no—
731C2×C8C23×D6112yes—
732C2×C8C23×D6112yes—
733C4⋊C4—24no—
734C4⋊C4—21no—
735C4⋊C4—614no—
736C4⋊C4—612no—
737C4⋊C4—1224no—
738C4⋊C4—1224no—
739C4⋊C4—1224no—
740C4⋊C4—1224no—
741C4⋊C4—1224no—
742C4⋊C4—1221no—
743C4⋊C4—1224no—
744C4⋊C4C23×D6112yes—
745C22⋊C4—24no—
746C22⋊C4—614no—
747C22⋊C4—614no—
748C22⋊C4—1224no—
749C22⋊C4—1224no—
750C22⋊C4—1224no—
751C22⋊C4—1224no—
752C22⋊C4—1224no—
753C42—612no—
754C42—612no—
755C42—1224no—
756C42—1224no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—614no—
765C23—612no—
766C23—1222no—
767C23—1222no—
768C23C2×D4×D6112yes—
769C23C2×D4×D6111yescharacteristic
770Q8—22no—
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—42no—
775Q8—614no—
776Q8—1222no—
777Q8—1224no—
778Q8—1222no—
779Q8—1222no—
780Q8—1222no—
781Q8—1222no—
782Q8—2448no—
783Q8—2448no—
784Q8—2448no—
785Q8—2442no—
786Q8—2442no—
787Q8C2×D4×D6114yes—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—1228no—
793D4—2448no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—48no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—612no—
806C2×C4—612no—
807C2×C4—612no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1224no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1224no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—2448no—
820C2×C4—2448no—
821C2×C4—2448no—
822C2×C4—2442no—
823C2×C4—2442no—
824C2×C4—2442no—
825C2×C4C2×D4×D6112yes—
826C2×C4C2×D4×D6112yes—
827C2×C4C2×D4×D6111yescharacteristic
828C2×C4#1451982212yes—
829C2×C4C24×D6111yescharacteristic
830C8—22no—
831C8—22no—
832C8—614no—
833C8—1222no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—44no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—84no—
842C22—614no—
843C22—1222no—
844C22—1222no—
845C22—1228no—
846C22#1684039412yes—
847C22#137×D6112yes—
848C22#1684057612yes—
849C22C22×D4×D6111yescharacteristic
850C4—22no—
851C4—24no—
852C4—42no—
853C4—42no—
854C4—1222no—
855C4—1224no—
856C4—1222no—
857C4—1222no—
858C4—2442no—
859C4—2442no—
860C4—2442no—
861C4#1684039412yes—
862C4C22×D4×D6111yescharacteristic
863C4C2×#1451982211yescharacteristic
864C2—42no—
865C2—82no—
866C2—1224no—
867C2#2145738714yesdirect product factor
868C2C2×#1684039411yescharacteristic
869C2C2×#137×D6111yescharacteristic
870C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
prime radicalC2×#16840419C2
hypercenterC2×#452D61
hypocenterC61C2×#3270
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#14519807C2semidirect
2. C22×Q16×D61C2semidirect
3. C2×#16840425C2semidirect
5. #21457387C2direct (N × H)
6. C2×#16840153C2semidirect
7. C2×#16840018C2semidirect
8. C2×#16839990C2semidirect
9. C2×#16839983C2semidirect
10. C2×#16839970C2semidirect
11. C2×#16839920C2semidirect
12. C2×#16839919C2semidirect
13. C2×#16839899C2semidirect
14. C2×#16839866C2semidirect
15. C2×#16839836C2semidirect
16. C2×C61×#452C2semidirect
21. C2×#14519807C22semidirect
28. C2×Q16×D61C22semidirect
34. #16840425C22semidirect
53. #16840153C22semidirect
54. #16840018C22semidirect
55. #16839990C22semidirect
56. #16839983C22semidirect
57. #16839970C22semidirect
58. #16839920C22semidirect
59. #16839919C22semidirect
60. #16839899C22semidirect
61. #16839866C22semidirect
62. #16839836C22semidirect
75. C61×#452C22semidirect
110. C2×#11758202D4semidirect
295. #11758202C2×D4semidirect
332. C22×D61#137semidirect
414. C2×D61C2×#137semidirect
439. C2×#452D61semidirect
447. C2×C61#3270semidirect
497. #452C2×D61semidirect
514. C61C2×#3270semidirect
867. C2#21457387direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#145198072
C22×Q16×D612
C2×#168404252
C2×#168404192
#214573872
C2×#168401532
C2×#168400182
C2×#168399902
C2×#168399832
C2×#168399702
C2×#168399202
C2×#168399192
C2×#168398992
C2×#168398662
C2×#168398362
C2×C61×#4522
C2×#327061